Computed tomography (CT) is an imaging technology in which an array of detectors is used to collect data from probing energetic rays transmitted through or emitted from an imaged subject. The collected data (also referred to as projection data) of the detector array contain the spatially integrated effects of the attenuation of the beam going through the imaged subject, which in turn indirectly represent a view of the internal structural details, i.e., features, of the imaged subject.
Such projection can be taken from different angles in a plane to collect a more complete view of the imaged subject. CT is the set of methods whereby a sufficient set of projection data is mapped by a mathematical inversion transformation algorithm to reconstruct the original image of the subject on the plane of projection. Intensive data processing following a reconstruction algorithm is required to convert the raw projection data into a recognizable view of the internal features of the subject. The image data are generated from the structure information indirectly represented by the projections.
This is possible simply because of the Fourier Slice Theorem, which states generally that a projection view of an imaged subject is related by Fourier transformation to the spatial structure of the subject. More specifically, the one dimensional Fourier transform of a parallel projection at a given view angle θ is equivalent to a one-dimensional “slice” of the two-dimensional Fourier transform of the imaged subject, taken at the same angle θ in the frequency domain. The Fourier Slice Theorem allows the image to be reconstructed by Fourier transforming the collected data from parallel projection, assembling the transforms into a two-dimensional Fourier transform, and applying inverse Fourier transformation to the result. In practical applications this process may be implemented by some form of filtered back-projection, which applies inverse two dimensional Fourier transform on the Fourier transform of each projection, without waiting for the completion of the collection of all the projection data.
The resolution of the generated image will depend on the spacing of the projections in θ and the spacing of detectors. The more projections that are taken and the closer the detectors are placed to each other, the greater the resolution of the resulting image.
In practice, fan beam projections are used much more often than the parallel projection because of the simplicity of the configuration comprising a single point source of radiation from which emanates a fan-shaped beam. The detector array is situated along an arc whereby the angle between the rays from the radiation source and the adjacent detectors remains a constant. Fan beam projection also makes it possible to avoid rotating the source of radiation, as required in the case of parallel projection, and to achieve much faster data acquisition and longer life of the equipment. Usually fan beam projection can have detectors separated equi-angularly on a curve or equally spaced along a straight line.
CT techniques are valuable in a wide range of application areas where noninvasive and nondestructive examination of internal structures is needed. Medical applications include imaging of emissions from radioactive substances introduced into the subject (single photon emission CT, positron emission CT, etc.), as well as x-ray transmission CT. Non-medical applications include, for example, non-destructive testing and inspection, mineral deposit mapping (microseismic CT imaging), and three-dimensional image generation in electron microscopy.
The most frequently used fan beam back projection algorithms require the detectors to be either equally spaced on a straight line or situated equi-angularly on a curve. In order to strictly follow this requirement, usually one must rotate the detector bank for each angle of the projections. This detector rotation definitely limits the data acquisition speed.
Because of the restrictive spatial requirement of many applications, e.g., packaging space, overall size, or aperture shape or geometry of the subject image, it is desirable that the detector array be situated in very close proximity to and just outside of the perimeter, i.e., confining contour, of the subject image to save space for the overall image capture assembly or component. At the same time, all of the radiation sources and the detectors are static, therefore no rotating parts are necessary. This not only extends the life time of overall assembly or component, more importantly, it reduces the data acquisition time.
One such example of a space constrained use of CT is the photonic readout of an image in a focal plane array that is coupled pixel by pixel to an electro-optical, acousto-optic, or piezo-electric element. Such an array may comprise a set of detectors or pixels that have optical, electrical, acoustic, or other characteristics, which alter the transmission of a probing energetic ray.